# What is (-2,9) in polar coordinates?

$\left(r , \theta\right) = \left(\sqrt{85} , \arctan \left(- \frac{9}{2}\right) + \pi\right) \approx \left(9.22 , 1.79\right)$, where the $1.79$ is the angle measure in radians.
The polar coordinates $\left(r , \theta\right)$ of a point in the plane are related to the rectangular coordinates of the point by the equations ${r}^{2} = {x}^{2} + {y}^{2}$ and $\tan \left(\theta\right) = \frac{y}{x}$ (when $x \ne 0$).
Since the point whose rectangular coordinates are $\left(x , y\right) = \left(- 2 , 9\right)$ is in the 2nd quadrant of the plane, if we take $r = \sqrt{{x}^{2} + {y}^{2}} = \sqrt{4 + 81} = \setminus \sqrt{85}$, then we need to add $\pi$ radians to the output of the arctangent function to find the angle: $\theta = \arctan \left(\frac{y}{x}\right) + \pi = \arctan \left(\frac{9}{- 2}\right) + \pi = \arctan \left(- \frac{9}{2}\right) + \pi$.